CIE colorimetryThe colour equation

Condition 1: 2° bipartite visual field, central fixation and dark surround.

Matching (reference, primary) stimuli: Red (R): 700 nm, Green (G): 546,1 nm and Blue (B): 435,8 nm

C R G B ( ) + ( ) + ( )R G B

Colour matching experiment

CIE colorimetry

The colour equation Condition 2: Magnitude of the Matching

Stimuli: The units of the three primaries provide a colour match with an equienergetic white test stimulus:

Luminance of the R, G, B matching stimuli:

red: 1,0000 cd/m2 = 1 new R unitgreen: 4,5907 cd/m2 = 1 new G unitblue: 0,0601 cd/m2 = 1 new B unit

The colour equation

But

i.e.:

C R G B ( ) + ( ) + ( )R G B

C R G B(520 nm) ( ) ( ) + ( ) R G B

C R G B ( ) + ( ) + ( )R G B

Practical realization of negative matching stimulus

Tristimulus values and colour matching functions

r g b( ), ( ) ( ) and

wavelength, nm

rel.sens.

400 500 600 700

r2

g2

b2

Colour matches are additive

I f

C r( 1 1) ( ) + g ( ) + b ( )1 1 R G Ba n d

C r( 2 2) ( ) + g ( ) + b ( )2 2 R G Bt h e n :

C C r r( ( ( ) 1 2 1 2) + ) ( ) + ( g + g ) ( ) + ( b + b ) ( )1 2 1 2 R G B

Additivity: Complex spectrum

R k P r

G k P g

B k P b

( ) ( )

( ) ( )

( ) ( )

380 nm

780 nm

380 nm

780 nm

380 nm

780 nm

Additivity: Complex spectrum

or as integrals

nm 780

nm 380

nm 780

nm 380

nm 780

nm 380

d)()(

,d)()( ,d)()(

bPkB

gPkGrPkR

X,Y,Z colour space

CIE 1931 Standard Colorimetric Observer1.the tristimulus values of the colour stimulus of the

equienergetic spectrum should again be equal;

2.all the photometric information (luminance, if thestimulus is measured in radiance units) should bein a single value, i.e. one of the colour matchingfunctions should be equal with the V()-function;

3.the tristimulus values of all real colours should bepositive and the volume of the tetrahedron shouldbe as small as possible.

RGB - XYZ matrix transformation

B

G

R

Z

Y

X

59427,505651,000000,0

06010,059070,400000,1

13016,175175,176888,2

The inverse transformation:

0,41846 -0,15866 -0,08283

-0,09117 0,25243 0,01571

0,00092 -0,00255 0,17860

The colour matching functions

wavelength, nm

rel.

sen

s.

0,00

0,20

0,40

0,60

0,80

1,00

1,20

1,40

1,60

1,80

350 400 450 500 550 600 650 700 750 800 850

x2(lambda)

y2(lambda)

z2(lambda)

The tristimulus values

T h e X , Y , Z t r is t im u lu s v a lu e s o f a c o lo u r s t im u lu s

(S ( ) ) :

X k S x Y k S y

Z k S z

( ) ( ) , ( ) ( ) ,

( ) ( )

d d

d

3 8 0 n m

7 8 0 n m

3 8 0 n m

7 8 0 n m

3 8 0 n m

7 8 0 n m

w ith k = 6 8 3 lm /W fo r p h o to m e tr ic q u a n t i t ie s .

Chromaticity co-ordinates

ZYX

Zz

ZYX

Yy

ZYX

Xx

, ,

where, as x + y + z = 1

Chromaticity diagram

E: equi-energy chromaticity

R, G, B: chromaticity of real primaries

x2

y2

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0,8

0,9

0 0,2 0,4 0,6 0,8 1 1,2 1,4 1,6 1,8

G

R

B

500

480

520

540

560

580

600620

460

E

Mixing and visualising colours in the chromaticity diagram

achromatic (N for neutral) "white point”dominant (complementary) wavelength

(D), correlate of hue

excitation purity, correlate of saturation

Excitation purity

For chromaticity point Cpe=(yC - yN)/(yDW - yN) or

pe=(xC - xN)/(xDW - xN)

x

y

0

0 , 1

0 , 2

0 , 3

0 , 4

0 , 5

0 , 6

0 , 7

0 , 8

0 , 9

0 0 , 2 0 , 4 0 , 6 0 , 8 1 1 , 2 1 , 4 1 , 6 1 , 8

5 0 0

4 8 0

5 2 0

5 4 0

5 6 0

5 8 0

6 0 06 2 0

4 6 0

NC

D W

C W

7 0 0

3 8 0

C '

P

Description of a colour stimulus

Tristimulus values, X, Y, Z.Chromaticity and luminance:

Y (or L), x, y.Further descriptors:

Luminance: L, dominant (or complementary) wavelength:D

excitation purity: pe

Additive mixture of two stimuli

X = aRXR + aGXG ;

Y = aRYR + aGYG ;

Z = aRZR + aGZG

.x

a X a X

a X Y Z a X Y Z

ya Y a Y

a X Y Z a X Y Z

R R G G

R( R R R G( G G G

R R G G

R( R R R G( G G G

+

+ +

+

+ +

) )

) )

CIE 1964 Standard Colorimetric Observer

Macula lutea or yellow spot10° filed of vision

.

.

nm 780

nm 380

1010

nm 780

nm 380

1010

nm 780

nm 380

1010

d)()(

,d)()( ,d)()(

zSkZ

ySkYxSkX

k = Y10

a n d

xX

X Y Zy

Y

X Y Zz

Z

X Y Z1010

10 10 1010

10

10 10 1010

10

10 10 10

, ,

CIE 1931 and 1964 Standard Colorimetric Observers

wavelength, nm

0,00E +00

5,00E -01

1,00E +00

1,50E +00

2,00E +00

2,50E +00

350 400 450 500 550 600 650 700 750 800 850

x10

y10

z10

x2

y2

z2

MacAdam ellipses

The CIE x,y diagram with ellipses representing small colour differences

The CIE system of colorimetry

CIE 1976 uniform chromaticity diagram colour temperature, Tc & correlated Tc,

TCCColorimetry of surface colours

CIE standard illuminants and sourcesCIE colour spaces

CIELUV space CIELAB space CIE 1994 colour difference

Brightness - luminance ratio

Uniform colour scales

u' = 4X / (X+15Y+3Z) = 4x / (-2x+12y+3)

v' = 9Y / (X+15Y+3Z) = 9y / (-2x+12y+3)

u = u' , v = (2/3)v'

CIE 1976 u,v hue angle:

huv = arctg[(v' - v'n) / (u' - u'n)] = v* / u*

The CIE 1976 u,v saturation:

suv = 13[(u' - u'n)2 + (v' - v'n)2]1/2

u’,v’ chromaticity diagram

u '

v'

0

0 ,1

0 ,2

0 ,3

0 ,4

0 ,5

0 ,6

0 0 ,1 0 ,2 0 ,3 0 ,4 0 ,5 0 ,6 0 ,7 0 ,8 0 ,9 1

S n

C

h u v

4 0 0

4 5 0

5 0 0

5 5 06 0 0

6 5 0

7 0 0

Colour temperature - 1

The spectral power distribution of a full radiator can be calculated using Planck's formula:

Me = c1-5[exp(c2/T)-1]-1

c2 = 1,4388x10-2 mK

Colour temperature - 2

x

0

0 ,1

0 ,2

0 ,3

0 ,4

0 ,5

0 ,6

0 ,7

0 ,8

0 ,9

0 0 ,2 0 ,4 0 ,6 0 ,8 1 1 ,2 1 ,4 1 ,6 1 ,8

6 5 0

6 0 0

5 5 0

5 0 0

4 8 0

1 0 0 .0 0 0 K

1 0 .0 0 0 K

6 5 0 0 KE

4 0 0 0 K2 8 5 6 K

2 0 0 0 K

Colorimetry of surface colours

radiance factor tristimulus values:

nm 780

nm 380

nm 780

nm 380

nm 780

nm 380

d)()()(

,d)()()( ,d)()()(

zSkZ

ySkYxSkX

d)()(

1

ySk

CIE Standard sources and illuminants - 1

CIE Standard Illuminant A: An illuminant having the same relative spectral power distribution as a Planckian radiator at a temperature of 2856 K

CIE Standard Illuminant C: An illuminant representing average daylight with a correlated colour temperature of about 6800 K. (This illuminant is now obsolete.)

CIE Standard sources and illuminants - 2,

daylight illuminants

for correlated colour temperatures from approximately 4000 K to 7000K:

244063,010

09911,010

9678,210

6070,4c

3

2c

6

3c

9

D TTT

x

yD = -3,000xD2 + 2,870xD - 0,275

CIE Standard sources and illuminants - 3, daylight illuminants

for correlated colour temperatures from 7000K to approximately 25 000 K

237040,010

24748,010

9018,110

0064,2c

3

2c

6

3c

9

D TTT

x

yD = -3,000xD2 + 2,870xD - 0,275

CIE Standard sources and illuminants - 4, daylight illuminants

S = S0() + M1S1 + M2S2

DD

DD2

DD

DD1

7341,00,2562+0,0241

0717,304424,310300,0

7341,00,2562+0,0241

9114,57703,13515,1

yx

yxM

yx

yxM

CIE Standard sources and illuminants - 5, daylight illuminants

CIE Standard Illuminant D65: An illuminant representing a phase of daylight with a correlated colour temperature of approximately 6500 K

CIE Illuminants: Fluorescent lamps

CIE Standard Illuminants

0

50

100

150

200

250

300

300 350 400 450 500 550 600 650 700 750 800 850

Wavelegth, nm

Rel

ativ

e sp

ectr

al p

ow

er d

istr

ibu

tio

n

Ill.A

Ill.D65

CIE D65 simulator

Correlated colour temperature

Iso-temperature lines (in u,v-diagram)

Different temperature concepts

Real temperatureRadiant temperatureDistribution temperatureColour temperature

Correlated colour temperature

Further recommendations on surface colour measurement

Standard of reflectance factor: perfect reflecting diffuser secondary reference reflectance factor

pressed barium sulphate plate“ halon" white standards

Standard measuring geometry 45°/normal reflectance factor diffuse/normal, specular included/excluded: reflectance

factor normal/diffuse, specular included/excluded: reflectance

CIE 1976 (L*a*b*) colour space, CIELAB colour space

L* 116(Y/Yn)1/3 - 16

a* 500 ( X/Xn)1/3 - (Y/Yn)1/3

b* 200 (Y/Yn)1/3 - (Z/Zn)1/3

for X/Xn > 0,008856

Y/Yn > 0,008856

Z/Zn > 0,008856

CIE 1976 a,b colour difference and CIELAB components

Colour difference: Eab (L*)2 + (a*)2

CIE1976 a,b chroma: Cab* (a*2 + b*2)1/2

CIE 1976 a,b hue-angle: ha arctan (b*/a*)

CIE 1976 a,b hue-difference: Hab* (Eab*)2 - (L*)2 - (Cab*)

21/2

CIE 1994 colour difference

k parametric factors, industry dependentS weighting functions, depend on

location in colour space:

EL

k S

C

k S

H

k S94

2 2 21 2

**

/

L L

ab*

C C

ab*

H H

2.2 Reference conditions

Reference conditions describe a set of experimental and material variables that are typical of

the conditions used in developing visual colour-difference data sets for object colours. The

reference conditions may not have been universally employed in all data sets used by CIE

TC1-47 in developing and testing the recommended model but they represent common levels

of the experimental variables. The reference conditions are:

CIE 2000 colour difference equation

2.2 Reference conditions

Reference conditions describe a set of experimental and material variables that are typical of

the conditions used in developing visual colour-difference data sets for object colours. The

reference conditions may not have been universally employed in all data sets used by CIE

TC1-47 in developing and testing the recommended model but they represent common levels

of the experimental variables. The reference conditions are:

Reference conditionsIllumination: source simulating the spectral relative irradiance of CIE Standard Illuminant D65.

Illuminance: 1000 lx.

Observer: normal colour vision.

Background field: uniform, neutral gray with L* = 50.

Viewing mode: object.

Sample size: greater than 4 degrees subtended visual angle.

Sample separation: minimum sample separation achieved by placing the sample pair in direct edge contact.

Sample colour-difference magnitude: 0 to 5 CIELAB units.

Sample structure: homogeneous colour without visually apparent pattern or non-uniformity.

Notes

Deviations from the reference conditions can affect the performance of the colour-difference model.

-Changes in viewing and illuminating conditions affect the validity of CIELAB as a colour space and further necessitate the definition of parametric factors.

- Changes in the source correlated colour temperature from 6500 K affect the accuracy of the chromatic adaptation transformation embedded in CIELAB, i. e. X/Xn, Y/Yn, and Z/Zn.

- Illuminance levels much lower than 1000 lux result in reduced discrimination. With an increase in the angle subtended by the colour-difference pair, the influence of background lightness on colour discrimination decreases.

Modification of the a* (red-green opponent) axis

The CIE 1976 (L*a*b*) colour space (CIE, 1986) is retained as an approximate uniform colour space representing perceptual colour magnitudes in terms of opponent colour scales with a

localized modification to the a* (red-green opponent) axis. This modification was made to improve agreement with visual colour-difference-perception for neutral colours. The modification increases the magnitudes of a’ values compared to a* values for colours at low chroma. At higher chroma the modified a’ value approaches the conventional a* value. Quantities L’ and b’ are defined as equal to L* and b* respectively. Primed quantities in this report refer to quantities derived from L’, a’, b’ coordinates.

Modification of the a* (red-green opponent) axis

L’=L* a’ = a*(1 + G) b’ = b*

where G depends on mean C* value of the two samples

Modified chroma and hue angle are calculated using the a’, b’ coordinates, but should not be used in colour space calculaqtions

Total colour-difference

A perceived visual colour-difference magnitude, DeltaV, is related to the total colour difference, DeltaE00, through an overall sensitivity factor, kE.

Delta V = kE-1Delta E00

Total colour difference

The total colour-difference between two colour samples with lightness, chroma and hue differences, with weighting functions, SL, SC, SH, parametric factors, kL, kC, kH and rotation function is determined similarly as CIE94 including this rotation factor

Rotation function

Visual colour-difference perception data show an interaction between chroma difference and hue difference in the blue region. The interaction results in a significant tilt of the major axis of the colour-difference ellipse. The ellipse tilt is in the counter-clockwise direction and away from the direction of constant hue angle. To account for this effect, a rotation function is applied to weighted hue and chroma differences.

The rotation function has a significant effect only for

the blue high chroma region of the a’, b’ plane.

Parametric factors

Parametric factors, kL, kC, kH, are correction terms for variation in perceived colour-difference component sensitivity with variation in experimental conditions. Under the reference conditions the parametric factors have assigned values of unity and do not affect the total colour difference.

In the textile industry it is common practice to set the lightness parametric factor to 2.

Metamerism

Different spectra, identical tristimulus values

Metamerism indices: Illuminant Observer

CIE Whiteness formulae

Whiteness:W Y + 800(xn-x) + 1700(yn - y)

Tint:

TW 1000 (xn-x) + 650(yn - y)

Advanced colorimetry

Colour appearance models chromatic adaptation

vonKries transformationCIE (Nayatani) proposalBradford transformation

Hunt model CIECAM97s model

Colour management

Brightness/Luminance

Chromatic versus achromatic signal brightness

Ware-Covan correction

L** = log(L) +C

C=0.256 - 0.184y - 2.527 xy + +4.656x3y + 4.657xy4

Contour lines of equiluminous lights of equal brightness

CIECAM97s model

ComprehensiveWide range of stimuli: dark to brightWide range of adapting intensities and

viewing conditions, degree of adaptationBased on x,y,z functionsPredictions: hue-angle, -quadrature,

brightness, lightness, saturation, chroma, colourfulness

Reverse modeSimplified and complete modelVersion for unrelated colours

CIECAM97s model

Input data Adapting field luminance, LA

Tristim.values of sample in source condition Source white in source condition Rel.lum. Of source background in s.cond.,Yb

Inpact of surround, chromatic induction, lightness contrast factor

Viewing condition

CIECAM97s model

Chromatic adaptation spectrally sharpened cone responses modified vonKries: degree of adapt.

Induction factor calculationsNon-linear response compressionAppearance correlates

red-green, yellow-blue - hue angle & quadr. Lightness, brightness colourfulness, chroma, saturation

Signal colours

Colorimetry of materials

Fluorescing materials photo-fluorescence luminophores - phosphors optical brighteners

Measurement reflected radiance factor emitted radiance factor total radiance factor

Spectral radiance factor

Two monochromator method for measuring total radiance factor

CIE standards and recommendations

ISO/CIE 10526-1991: Colorimetric illuminants ISO/CIE 10526-1991: Colorimetric observersCIE 13.3-1988: Colour renderingCIE 15.2-1986: ColorimetryCIE 17.4: International lighting vocabularyCIE 51-1981: Quality of daylight simulators

CIE TCs working on colorimetry

CIECAM colour appearance modelsVDU - Reflective media comparisonChromaticity diagram with

physiologically significant axesGeometric tolerances in colorimetryUpdating the colorimetry and colour

rendering documents